Ultra-low-loss coupled-core multicore optical fibers

ABSTRACT

A coupled-core multicore optical fiber has a plurality of cores that are doped with alkali metals or chlorine to achieve low attenuation and a large effective area. The cores may be embedded in a common cladding region that may be fluorine doped. The cores may also be doped with chlorine, either with the alkali metals described above or without the alkali metals.

This Application is a divisional of U.S. Pat. Application Serial No.17/387,113, filed on Jul. 28, 2021, which claims priority under 35 USC§119(e) from U.S. Provisional Pat. Application Serial Number 63/063,559filed on Aug. 10, 2020, which is incorporated by reference herein in itsentirety.

BACKGROUND Field

The present disclosure pertains to optical fibers. More particularly,the present disclosure relates to coupled-core multicore optical fibershaving a plurality of cores that are doped with alkali metals and/orchlorine to achieve low attenuation and a large effective area.

Technical Background

The transmission capacity through single-mode optical fiber hastheoretically reached its fundamental limit of around 100 Tb/s/fiber.Transmitting even 80 Tb/s in a single-mode optical fiber overtransoceanic distance has proven challenging in the absence of animproved optical signal-to-noise ratio (OSNR). The actual capacity limitover about 10,000 km of a submarine single-mode optical fiber systemused in a transoceanic transmission system is only about 50 Tb/s, evenwith advanced ultra-low-loss and low-nonlinearity optical fibers.

Spatial division multiplexing (SDM) technologies are being studiedintensively to overcome this capacity limit. Transmission capacity maybe increased by increasing the fiber pair count in the cable, increasingthe capacity of each fiber, or increasing both. However, in submarinecables, higher fiber counts have limited practicality because a thickerand heavier cable significantly increases the cable installation costdue to the limited loading capacities of the ships that deploy thecables.

Multicore fiber (MCF) may exhibit less transmission loss when used intransoceanic applications. However, for practical use in ultra-long-haulsubmarine systems, the MCF should have ultra-low loss (i.e., lowattenuation) to produce a high OSNR, have high spatial-mode density toincrease the spatial channel count, and enable low differential groupdelay (DGD) between spatial modes to decrease the digital signalprocessing complexity. Also, the standard cladding diameter of 125 µmshould be maintained so that no major modifications are needed forinstallation of the cable.

SUMMARY

Thus, there is a need for new optical fibers that solve the problemsdescribed above while having satisfactory attenuation and an increasedtransmission capacity.

In a first aspect, either alone or in combination with any other aspect,a coupled-core multicore optical fiber includes an outer common claddingcomprising a relative refractive index Δ_(OCC) relative to pure silica;and a plurality of cores disposed in the outer common cladding, each ofthe plurality of cores comprising a relative refractive index Δ_(Ci)relative to pure silica and a maximum relative refractive index A_(CLi)relative to pure silica. For the coupled-core multicore optical fiberA_(CLi) > Δ_(Ci) > Δ_(OCC). Each of the plurality of cores has aneffective area at 1550 nm of greater than or equal to 120 micrometers²(µm²) and less than or equal to 160 µm². A coupling coefficient Kbetween adjacent cores of the plurality of cores is greater than orequal to 1 × 10⁻³ /m.

In a second aspect, either alone or in combination with any otheraspect, a coupled-core multicore optical fiber includes an outer commoncladding comprising a relative refractive index Δ_(OCC) relative to puresilica; and a plurality of cores disposed in the outer common cladding,each of the plurality of cores comprising an inner core portioncomprising a relative refractive index Δ_(Ci) relative to pure silicaand a maximum relative refractive index A_(CLi) relative to pure silica.For the coupled-core multicore optical fiber A_(CLi) > Δ_(Ci) > Δ_(OCC).Each of the inner core portions comprises greater than or equal to 0.02wt.% and less than or equal to 0.15 wt.% fluorine. A distance betweencenters of an adjacent two of the plurality of cores is greater than orequal to 20 micrometers (µm) and less than or equal to 40 µm. A couplingcoefficient K between adjacent cores in the plurality of cores isgreater than or equal to 1 × 10⁻³ /m.

In a third aspect, either alone or in combination with any other aspect,a distance between centers of an adjacent two of the plurality of coresis greater than or equal to 45 µm and less than or equal to 65 µm.

In a fourth aspect, either alone or in combination with the thirdaspect, a crosstalk between the plurality of cores is greater than orequal to -50 decibels (dB) per kilometer.

In a fifth aspect, either alone or in combination with any other aspect,the coupled-core multicore optical fiber includes greater than or equalto 2 and less than or equal to 6 of the cores.

In a sixth aspect, either alone or in combination with the fifth aspect,the coupled-core multicore optical fiber includes 3 sets of 3 of thecores.

In a seventh aspect, either alone or in combination with any otheraspect, a cable cutoff wavelength of each of the plurality of cores ofthe optical fiber is greater than or equal to 1200 nanometers (nm) andless than or equal to 1520 nm.

In an eighth aspect, either alone or in combination with the seventhaspect, an average bend loss of the plurality of cores of the opticalfiber at a wavelength of 1550 nm measured on a mandrel having a diameterof 20 millimeters (mm) is greater than or equal to 0.01 decibels perturn (dB/turn) and less than or equal to 1 dB/turn.

In a ninth aspect, either alone or in combination with any other aspect,an average bend loss of the plurality of cores of the optical fiber at awavelength of 1550 nm measured on a mandrel having a diameter of 30 mmis greater than or equal to 0.001 decibels per turn (dB/turn) and lessthan or equal to 0.03 dB/turn.

In a tenth aspect, either alone or in combination with any other aspect,a minimum distance between a center of one of the plurality of cores toan adjacent edge of the optical fiber along a line formed by acenterpoint of the optical fiber, the center of the one of the pluralityof cores, and the adjacent edge in a plane perpendicular to a long axisof the coupled-core multicore optical fiber is greater than or equal to30 µm and less than or equal to 50 µm.

In an eleventh aspect, either alone or in combination with any otheraspect, each of the plurality of cores comprises an inner core portionsurrounded by an inner cladding portion.

In a twelfth aspect, either alone or in combination with any otheraspect, each inner cladding portion comprises a relative refractiveindex Δ_(ICi), the inner core portion comprises the A_(CLi), andΔ_(CLi) > A_(Ci) > Δ_(ICi) > Δ_(OCC).

In a thirteenth aspect, either alone or in combination with any otheraspect, each of the plurality of cores comprises an inner claddingportion and an inner core portion corresponding to the inner claddingportion, each inner cladding portion surrounding the corresponding innercore portion.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary and are intendedto provide an overview or framework to understand the nature andcharacter of the claims. Additional features and advantages will be setforth in the detailed description which follows, and in part will bereadily apparent to those skilled in the art from the description orrecognized by practicing the embodiments as described in the writtendescription and claims hereof, as well as the appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings are illustrative of selected aspects of thepresent disclosure, and together with the description serve to explainprinciples and operation of methods, products, and compositions embracedby the present disclosure, in which:

FIG. 1 schematically depicts an optical system including a signalsource, a multicore optical fiber, and a photodetector, according to oneor more embodiments shown and described herein;

FIG. 2 schematically depicts a multicore optical fiber, according to oneor more embodiments shown and described herein;

FIG. 3 schematically depicts an X-Y cross-section of the multicoreoptical fiber of FIG. 2 taken along the line 3-3, according to one ormore embodiments shown and described herein;

FIG. 4 schematically depicts an X-Y cross-section of an exemplary coreand inner cladding of a multicore optical fiber, according to one ormore embodiments shown and described herein;

FIG. 5A schematically depicts an X-Y cross-section of an alternativemulticore optical fiber of FIG. 2 along section 3-3 having four cores, acommon inner cladding, and a common outer cladding according to one ormore embodiments shown and described herein;

FIG. 5B schematically depicts an X-Y cross-section of an alternativemulticore optical fiber of FIG. 2 along section 3-3 having four cores,four inner claddings, and a common outer cladding according to one ormore embodiments shown and described herein;

FIG. 6A schematically depicts an X-Y cross-section of an alternativemulticore optical fiber of FIG. 2 along section 3-3 having three cores,according to one or more embodiments shown and described herein;

FIG. 6B schematically depicts an X-Y cross-section of an alternativemulticore optical fiber of FIG. 2 along section 3-3 having three cores,according to one or more embodiments shown and described herein;

FIG. 6C schematically depicts an X-Y cross-section of an alternativemulticore optical fiber of FIG. 2 along section 3-3 having six cores,according to one or more embodiments shown and described herein;

FIG. 6D schematically depicts an X-Y cross-section of an alternativemulticore optical fiber of FIG. 2 along section 3-3 having threeclusters of three cores, according to one or more embodiments shown anddescribed herein;

FIG. 7A graphically depicts a relative refractive index profile of asingle core, inner common cladding, and outer common cladding of anoptical fiber preform from which a coupled-core multicore fiber may bedrawn, according to one or more embodiments shown and described herein;

FIG. 7B graphically depicts a relative refractive index profile of asingle core, inner cladding, and outer common cladding of an opticalfiber preform from which a coupled-core multicore fiber may be drawn,according to one or more embodiments shown and described herein;

FIG. 8 graphically depicts a relative refractive index profile of asingle core, inner cladding, inner common cladding, and outer commoncladding of the coupled-core multicore fiber of Example 1, according toone or more embodiments shown and described herein;

FIG. 9 graphically depicts a relative refractive index profile of asingle core, inner common cladding, and outer common cladding of thecoupled-core multicore fiber of Example 2, according to one or moreembodiments shown and described herein;

FIG. 10 graphically depicts a relative refractive index profile of asingle core, inner common cladding, and outer common cladding of thecoupled-core multicore fiber of Example 3, according to one or moreembodiments shown and described herein;

FIG. 11 graphically depicts a relative refractive index profile of asingle core, inner common cladding, and outer common cladding of thecoupled-core multicore fiber of Example 4, according to one or moreembodiments shown and described herein;

FIG. 12 graphically depicts a relative refractive index profile of asingle core, inner common cladding, and outer common cladding of thecoupled-core multicore fiber of Example 5, according to one or moreembodiments shown and described herein; and

FIG. 13 graphically depicts a relative refractive index profile of asingle core, inner common cladding, and outer common cladding of thecoupled-core multicore fiber of Example 6, according to one or moreembodiments shown and described herein.

DETAILED DESCRIPTION

In this specification and in the claims which follow, reference will bemade to a number of terms which shall be defined to have the followingmeanings:

As used herein, the term “about” means that amounts, sizes,formulations, parameters, and other quantities and characteristics arenot and need not be exact, but may be approximate and/or larger orsmaller, as desired, reflecting tolerances, conversion factors, roundingoff, measurement error and the like, and other factors known to those ofskill in the art. When the term “about” is used in describing a value oran end-point of a range, the disclosure should be understood to includethe specific value or end-point referred to. Whether or not a numericalvalue or end-point of a range in the specification recites “about,” thenumerical value or end-point of a range is intended to include twoembodiments: one modified by “about,” and one not modified by “about.”It will be further understood that the end-points of each of the rangesare significant both in relation to the other end-point, andindependently of the other end-point.

A multicore optical fiber, also referred to as a multicore fiber or“MCF”, is considered for the purposes of the present disclosure toinclude two or more core fibers disposed within a cladding matrix. Eachcore fiber can be considered as having a higher index core surrounded bya lower index cladding matrix defining a common cladding. Optionally,each core fiber can include a higher index core surrounded by one ormore lower index inner claddings disposed between each core and thecladding matrix of the common cladding. As used herein, the term “innercore portion” refers to the higher index core. That is, a core fiber mayinclude an inner core portion and optionally one or more lower indexinner claddings.

“Radial position” and/or “radial distance,” when used in reference tothe radial coordinate “r” refers to radial position relative to thecenterline (r = 0) of each individual core in a multicore optical fiber.“Radial position” and/or “radial distance,” when used in reference tothe radial coordinate “R” refers to radial position relative to thecenterline (R = 0, central fiber axis) of the multicore optical fiber.The length dimension “micrometer” may be referred to herein as micron(or microns) or µm.

The “refractive index profile” is the relationship between refractiveindex or relative refractive index and radial distance r from the core’scenterline for each core fiber of the multicore optical fiber. Forrelative refractive index profiles depicted herein as having stepboundaries between adjacent core and cladding regions, normal variationsin processing conditions may result in step boundaries at the interfaceof adjacent regions that are not sharp. It is to be understood thatalthough boundaries of refractive index profiles may be depicted hereinas step changes in refractive index, the boundaries in practice may berounded or otherwise deviate from perfect step function characteristics.It is further understood that the value of the relative refractive indexmay vary with radial position within the core region and/or any of thecladding regions. When relative refractive index varies with radialposition in a particular region of the fiber (core region and/or any ofthe cladding regions), it may be expressed in terms of its actual orapproximate functional dependence or in terms of an average valueapplicable to the region. Unless otherwise specified, if the relativerefractive index of a region (core region and/or any of the inner and/orcommon cladding regions) is expressed as a single value, it isunderstood that the relative refractive index in the region is constant,or approximately constant, and corresponds to the single value or thatthe single value represents an average value of a non-constant relativerefractive index dependence with radial position in the region. Whetherby design or a consequence of normal manufacturing variability, thedependence of relative refractive index on radial position may besloped, curved, or otherwise non-constant.

The “relative refractive index” or “relative refractive index percent”as used herein with respect to multicore optical fibers and fiber coresof multicore optical fibers is defined according to equation (1):

$\begin{matrix}{\Delta\% = 100\frac{n^{2}(r) - n_{c}^{2}}{2n^{2}(r)}} & \text{­­­(1)}\end{matrix}$

where n(r) is the refractive index at the radial distance r from thecore’s centerline at a wavelength of 1550 nm, unless otherwisespecified, and n_(c) is 1.444, which is the refractive index of undopedsilica glass at a wavelength of 1550 nm. As used herein, the relativerefractive index is represented by Δ (or “delta”) or Δ% (or “delta %)and its values are given in units of “%” or “%Δ”, unless otherwisespecified. Relative refractive index may also be expressed as Δ(r) orΔ(r)%. When the refractive index of a region is less than the referenceindex n_(c), the relative refractive index is negative and can bereferred to as a trench. When the refractive index of a region isgreater than the reference index n_(c), the relative refractive index ispositive and the region can be said to be raised or to have a positiveindex.

The average relative refractive index of a region of the multicoreoptical fiber can be defined according to equation (2):

$\begin{matrix}{\Delta\%\,\text{=}\frac{\int_{r_{inner}}^{r_{outer}}{\Delta(r)dr}}{\left( {r_{outer}\text{-}r_{inner}} \right)}} & \text{­­­(2)}\end{matrix}$

where r_(inner) is the inner radius of the region, r_(outer) is theouter radius of the region, and Δ(r) is the relative refractive index ofthe region.

The term “α-profile” (also referred to as an “alpha profile”) refers toa relative refractive index profile Δ(r) that has the followingfunctional form (3):

$\begin{matrix}{\Delta(r) = \Delta\left( r_{0} \right)\left\{ {1 - \left\lbrack \frac{\left| {r - r_{0}} \right|}{\left( {r_{1} - r_{0}} \right)} \right\rbrack^{\alpha}} \right\}} & \text{­­­(3)}\end{matrix}$

where r_(o) is the point at which Δ(r) is maximum, r₁ is the point atwhich Δ(r) is zero, and r is in the range r_(i) ≤ r ≤ r_(f), where r_(i)is the initial point of the α-profile, r_(f) is the final point of theα-profile, and α is a real number. In some embodiments, examples shownherein can have a core alpha of 1 ≤ α ≤ 100. In practice, an actualoptical fiber, even when the target profile is an alpha profile, somelevel of deviation from the ideal configuration can occur. Therefore,the alpha parameter for an optical fiber may be obtained from a best fitof the measured index profile, as is known in the art.

The term “graded-index profile” refers to an α-profile, where α< 10. Theterm “step-index profile” refers to an α-profile, where α ≥ 10.

The “effective area” can be defined as (4):

$\begin{matrix}{A_{eff} = \frac{2\pi\left\lbrack {\int_{0}^{\infty}{\left( {f(r)} \right)^{2}rdr}} \right\rbrack^{2}}{\int_{0}^{\infty}{\left( {f(r)} \right)^{4}rdr}}} & \text{­­­(4)}\end{matrix}$

where f(r) is the transverse component of the electric field of theguided optical signal and r is radial position in the fiber. “Effectivearea” or “A_(eff)” depends on the wavelength of the optical signal.Specific indication of the wavelength will be made when referring to“Effective area” or “A_(eff)” herein. Effective area is expressed hereinin units of “µm²”, “square micrometers”, “square microns” or the like.

Unless otherwise noted herein, optical properties (such as dispersion,dispersion slope, etc.) are reported for the LP01 mode.

“Chromatic dispersion,” herein referred to as “dispersion” unlessotherwise noted, of an optical fiber is the sum of the materialdispersion, the waveguide dispersion, and the intermodal dispersion.“Material dispersion” refers to the manner in which the refractive indexof the material used for the optical core affects the velocity at whichdifferent optical wavelengths propagate within the core. “Waveguidedispersion” refers to dispersion caused by the different refractiveindices of the core and cladding of the optical fiber. In the case ofsingle mode waveguide fibers, the inter-modal dispersion is zero.Dispersion values in a two-mode regime assume intermodal dispersion iszero. The zero-dispersion wavelength (λ_(o)) is the wavelength at whichthe dispersion has a value of zero. Dispersion slope is the rate ofchange of dispersion with respect to wavelength. Dispersion anddispersion slope are reported herein at a wavelength of 1310 nm or 1550nm, as noted, and are expressed in units of ps/nm/km and ps/nm²/km,respectively. Chromatic dispersion is measured as specified by the IEC60793-1-42:2013 standard, “Optical fibres - Part 1-42: Measurementmethods and test procedures - Chromatic dispersion.”

The cutoff wavelength of an optical fiber is the minimum wavelength atwhich the optical fiber will support only one propagating mode. Forwavelengths below the cutoff wavelength, multimode transmission mayoccur and an additional source of dispersion may arise to limit thefiber’s information carrying capacity. Cutoff wavelength will bereported herein as a cable cutoff wavelength. The cable cutoffwavelength is based on a 22-meter cabled fiber length as specified inTIA-455-80: FOTP-80 IEC-60793-1-44 Optical Fibres — Part 1-44:Measurement Methods and Test Procedures — Cut—off Wavelength (21 May2003), by Telecommunications Industry Association (TIA).

The “theoretical cutoff wavelength”, or “theoretical fiber cutoff”, or“theoretical cutoff”, for a given higher-order mode, is the wavelengthabove which guided light cannot propagate in that higher-order mode.According to an aspect of the present disclosure, the cutoff wavelengthrefers to the cutoff wavelength of the LP11 mode. A mathematicaldefinition can be found in Single Mode Fiber Optics, Jeunhomme, pp.39-44, Marcel Dekker, New York, 1990, wherein the theoretical fibercutoff is described as the wavelength at which the mode propagationconstant becomes equal to the plane wave propagation constant in thecommon cladding. This theoretical wavelength is appropriate for aninfinitely long, perfectly straight fiber that has no diametervariations.

The bend resistance of an optical fiber, expressed as “bend loss”herein, can be gauged by induced attenuation under prescribed testconditions as specified by the IEC-60793-1-47:2017 standard, “Opticalfibres - Part 1-47: Measurement methods and test procedures-Macrobending loss.” For example, the test condition can entaildeploying or wrapping the fiber one or more turns around a mandrel of aprescribed diameter, e.g., by wrapping 1 turn around either a 15 mm, 20mm, or 30 mm or similar diameter mandrel (e.g. “1×15 mm diameter bendloss” or the “1×20 mm diameter bend loss” or the “1×30 mm diameter bendloss”) and measuring the increase in attenuation per turn.

The term “attenuation,” as used herein, is the loss of optical power asthe signal travels along the optical fiber. Attenuation is measured asspecified by the IEC 60793-1-40:2019 standard entitled “Optical fibres -Part 1-40: Attenuation measurement methods.”

As used herein, the multicore optical fiber can include a plurality ofcores, wherein each core can be defined as an i^(th) core (i.e., 1^(st),2^(nd), 3^(rd), 4^(th), etc). Each i^(th) core can have an outer radiusr_(Ci), an average relative refractive index Δ_(Ci), and a maximumrelative refractive index A_(CiMAX). Each i^(th) core is disposed withina cladding matrix of the multicore optical fiber, which defines an outercommon cladding of the multicore optical fiber. The outer commoncladding includes a relative refractive index Δ_(OCC) and an outerradius Rocc. Optionally, an inner common cladding may be disposed withinthe outer common cladding of the multicore optical fiber. The innercommon cladding includes a relative refractive index Δ_(ICC) and anouter radius R_(ICC). In embodiments in which the inner common claddingis not present, the refractive index of the outer common cladding istypically referred to as Δ_(CC) and the outer radius of the commoncladding is typically referred to as Rec.

Optionally, each i^(th) core includes a corresponding i^(th) centerlineregion that includes an outer radius r_(CLi) and maximum relativerefractive index Δ_(CLi). Thus, i=1 refers to a first core having anouter radius r_(C1) and relative refractive index Δ_(Cl) and acenterline region having an outer radius r_(CL1) and maximum relativerefractive index Δ_(CL1). When i=2, the core is referred to as a secondcore having an outer radius r_(C2) and relative refractive index Δ_(C2).When the second core includes a corresponding i^(th) centerline region,where i=2, it is referred to as the second centerline region andincludes an outer radius r_(CL2) and maximum relative refractive indexΔ_(CL2). Each additional i^(th) core and optional i^(th) inner claddingis referred to as a third core and optional centerline region (i=3), afourth core and optional fourth centerline region (i=4), etc... Thenumber assigned to each i^(th) core is used to distinguish one core fromanother for the purposes of discussion and does not necessarily implyany particular ordering of the cores.

Optionally, each i^(th) core is surrounded by a corresponding i^(th)inner cladding having a width δr_(ICi) and a relative refractive indexΔ_(ICi). Thus, i=1 refers to a first core having an outer radius r_(C1)and relative refractive index Δ_(C1). When the first core is surroundedby a corresponding i^(th) inner cladding, where i=1, it is referred toas the first inner cladding and has a width δr_(ICl) and a relativerefractive index Δ_(IC1). When i=2, the core is referred to as a secondcore having an outer radius r_(C2) and relative refractive index Δ_(C2).When the second core is surrounded by a corresponding i^(th) innercladding, where i=2, it is referred to as the second inner cladding andincludes a width δr_(IC2) and a relative refractive index Δ_(IC2). Eachadditional i^(th) core and optional i^(th) inner cladding is referred toas a third core and optional third inner cladding (i=3), a fourth coreand optional fourth inner cladding (i=4), etc... The number assigned toeach i^(th) core is used to distinguish one core from another for thepurposes of discussion and does not necessarily imply any particularordering of the cores.

According to one aspect of the present disclosure, the core forms thecentral portion of each core fiber within the multicore optical fiberand is substantially cylindrical in shape. In addition, when present,the surrounding inner cladding region is substantially annular in shape.Annular regions may be characterized in terms of an inner radius and anouter radius. Radial positions r refer herein to the outermost radii ofthe region (e.g., the core, the centerline region, the inner claddingregion, etc...). When two regions are directly adjacent to each other,the outer radius of the inner of the two regions coincides with theinner radius of the outer of the two regions. For example, inembodiments in which an inner cladding region surrounds and is directlyadjacent to a core region, the outer radius of the core region coincideswith the inner radius of the inner cladding region and the outer radiusof the inner cladding region is separated from the inner radius of theinner cladding region by the width δr_(IC).

An “up-dopant” is herein considered to be a substance added to the glassof the component being studied that has a propensity to raise therefractive index relative to pure undoped silica. A “down-dopant” isherein considered to be a substance added to the glass of the componentbeing studied that has a propensity to lower the refractive indexrelative to pure undoped silica. Examples of up-dopants include GeO₂(germania), Al₂O₃, P₂O₅, TiO₂, Cl, Br, and alkali metal oxides, such asK₂O, Na₂O, Li₂O, C_(S2)O, Rb₂O, and mixtures thereof. Examples ofdown-dopants include fluorine and boron.

The term “crosstalk” in a multi-core fiber is a measure of how muchpower leaks from one core to another, adjacent core. As used herein, theterm “adjacent core” refers to the core that is nearest to the referencecore. In embodiments, all cores may be equally spaced from one another,meaning that all cores are adjacent one another. In other embodiments,the cores may not be equally spaced from one another, meaning that somecores will be spaced further from the reference core than adjacent coresare spaced from the reference core. The crosstalk can be determinedbased on the coupling coefficient, which depends on the refractive indexprofile design of the core, the distance between the two adjacent cores,the structure of the cladding surrounding the two adjacent cores, andΔβ, which depends on a difference in propagation constant β valuesbetween the two adjacent cores. For two adjacent cores with power P₁launched into the first core, then the power P₂ coupled from the firstcore to the second core can be determined from coupled mode theory usingthe following equation (5):

$\begin{matrix}{P_{2} = \frac{L}{L_{c}}\left\langle {\left( \frac{\kappa}{g} \right)^{2}sin^{2}\left( {g\Delta L} \right)} \right\rangle P_{1}} & \text{­­­(5)}\end{matrix}$

where < > denotes the average, L is fiber length, K is the couplingcoefficient between the electric fields of the two cores, ΔL is thelength of the fiber, L_(c) is the correlation length, and g is given bythe following equation (6):

$\begin{matrix}{g^{2} = \kappa^{2} + \frac{\left( {\Delta\beta} \right)}{2}^{2}} & \text{­­­(6)}\end{matrix}$

where Δβ is the mismatch in propagation constants between the LP01 modesin the two adjacent cores when they are isolated. The crosstalk (in dB)is then determined using the following equation (7):

$\begin{matrix}{X = 10log\left( \frac{P_{2}}{P_{1}} \right) = 10log\left( {\frac{L}{L_{c}}\left\langle {\left( \frac{\kappa}{g} \right)^{2}sin^{2}\left( {g\Delta L} \right)} \right\rangle} \right)} & \text{­­­(7)}\end{matrix}$

The crosstalk between the two adjacent cores increases linearly withfiber length in the linear scale (equation (5)) but does not increaselinearly with fiber length in the dB scale (equation (7)). As usedherein, crosstalk performance is referenced to a 1 km length L ofoptical fiber. However, crosstalk performance can also be representedwith respect to alternative optical fiber lengths, with appropriatescaling. For optical fiber lengths other than 1 km, the crosstalkbetween cores can be determined using the following equation (8):

$\begin{matrix}{X(L) = X(100) + 10log(L)} & \text{­­­(8)}\end{matrix}$

For example, for a 10 km length of optical fiber, the crosstalk can bedetermined by adding “10 dB” to the crosstalk value for a 1 km lengthoptical fiber. For a 100 km length of optical fiber, the crosstalk canbe determined by adding “20 dB” to the crosstalk value for a 1 km lengthof optical fiber. For long-haul transmission in an uncoupled-coremulticore fiber, the crosstalk should be less than or equal to -50 dB,less than or equal to -60 dB, or even less than or equal to -70 dB. Forlong-haul transmission in a coupled-core multicore fiber, the crosstalkis greater than or equal to -40 dB, greater than or equal to -30 dB,greater than or equal to -20 dB, or even greater than or equal to -10dB. If the coupling coefficient is large enough, the power can coupleback and forth periodically between two cores along the fiber. In thiscase, the crosstalk does not scale with the fiber length, but changesperiodically. The crosstalk could even reach 100%, or zero dB.

Techniques for determining crosstalk between cores in a multicoreoptical fiber can be found in M. Li, et al., “Coupled Mode Analysis ofCrosstalk in Multicore Fiber with Random Perturbations,” in OpticalFiber Communication Conference, OSA Technical Digest (online), OpticalSociety of America, 2015, paper W2A.35, and Shoichiro Matsuo, et al.,“Crosstalk behavior of cores in multi-core fiber under bent condition,”IEICE Electronics Express, Vol. 8, No. 6, p. 385-390, published Mar. 25,2011 and Lukasz Szostkiewicz, et al., “Cross talk analysis in multicoreoptical fibers by supermode theory,” Optics Letters, Vol. 41, No. 16, p.3759-3762, published Aug. 15, 2016, the contents of which are allincorporated herein by reference in their entirety.

The phrase “coupling coefficient” K, as used herein, is related to theoverlap of electric fields when the two cores are close to each other.The square of the coupling coefficient, K², is related to the averagepower in core m as influenced by the power in other cores in themulticore optical fiber. The “coupling coefficient” can be estimatedusing the coupled power theory, with the methods disclosed in M.Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical Expressionof Average Power-Coupling Coefficients for Estimating IntercoreCrosstalk in Multicore Fibers,” IEEE Photonics J., 4(5), 1987-95 (2012);and T. Hayashi, T. Sasaki, E. Sasaoka, K. Saitoh, and M. Koshiba,“Physical Interpretation of Intercore Crosstalk in Multicore Fiber:Effects of Macrobend, Structure Fluctuation, and Microbend,” OpticsExpress, 21(5), 5401-12 (2013), the contents of which are incorporatedby reference herein in their entirety.

Directional terms as used herein - for example up, down, right, left,front, back, top, bottom - are made only with reference to the figuresas drawn and are not intended to imply absolute orientation.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order, nor that with any apparatus specificorientations be required. Accordingly, where a method claim does notactually recite an order to be followed by its steps, or that anyapparatus claim does not actually recite an order or orientation toindividual components, or it is not otherwise specifically stated in theclaims or description that the steps are to be limited to a specificorder, or that a specific order or orientation to components of anapparatus is not recited, it is in no way intended that an order ororientation be inferred, in any respect. This holds for any possiblenon-express basis for interpretation, including: matters of logic withrespect to arrangement of steps, operational flow, order of components,or orientation of components; plain meaning derived from grammaticalorganization or punctuation, and; the number or type of embodimentsdescribed in the specification.

As used herein, the singular forms “a,” “an” and “the” include pluralreferents unless the context clearly dictates otherwise. Thus, forexample, reference to “a” component includes aspects having two or moresuch components, unless the context clearly indicates otherwise.

The present description provides a coupled-core multicore optical fiberhaving a plurality of cores that are doped with alkali metals orchlorine to achieve low attenuation and a large effective area. Thecores may be embedded in an inner (or common inner) cladding region thatmay be fluorine doped, which may be surrounded by an outer (or commonouter) cladding, which may also be fluorine doped, with a total diameterof 125 µm or greater, such as for example about 200 µm. For instance,the total diameter may be greater than or equal to 125 µm and less thanor equal to 180 µm. In other embodiments, the cores may be doped withchlorine, either with the alkali metals described above or without thealkali metals.

Coupled-core multicore optical fiber is distinct from uncoupled-coremulticore optical fiber. In the uncoupled variety, the cores are meantto be spatially isolated from one another to limit crosstalk between thecores. Coupled-core multicore optical fibers, however, take advantage ofcrosstalk between the cores. As a result, the distance between cores(i.e., the “core pitch”) can be much smaller in coupled-core multicoreoptical fibers than in uncoupled-core multicore optical fibers, allowingfor more cores per unit area of the cross section of the multicoreoptical fiber.

Referring now to FIG. 1 , an optical system 100 comprising acoupled-core multicore optical fiber 110 with a plurality of cores C₁,C₂ (FIG. 2 ), a signal source 180, and a photon detector 190 isschematically depicted. The signal source 180 may produce multiplemodulated signals, S₁ and S₂, such as those produced by a distributedfeedback lasers (DFB) or vertical-cavity surface-emitting lasers(VCSEL). The coupled-core multicore optical fiber 110 comprises an inputend 112 optically coupled to the signal source 180 and an output end 114optically coupled to the photodetector 190 and an outer surface 116. Inoperation, the signal source 180 may selectively direct photons from onelaser into an individual core of the plurality of cores. For example,the signal source 180, the input end 112 of the coupled-core multicoreoptical fiber 110, or both, may be coupled to a multicore fan-in device,which is configured to align the signal source 180 with any individualcore of the plurality of cores. For example, the signal S₁ from signalsource 180 may be aligned with the core C₁ (FIG. 2 ) of the coupled-coremulticore optical fiber 110 and may direct a plurality of photons intothe core C₁, and the signal S₂ from signal source 180 may be alignedwith the core C₂ (FIG. 2 ) of the coupled-core multicore optical fiber110 and may direct a plurality of photons into the core C₂.

FIGS. 2 and 3 illustrate an isometric view of a section of acoupled-core multicore optical fiber 110 and a cross-sectional view ofthe coupled-core multicore optical fiber 110 along section 3-3 of FIG. 2, respectively. The coupled-core multicore optical fiber 110 includes acentral fiber axis 12 (the centerline of the coupled-core multicoreoptical fiber 110, which defines radial position R = 0) and a claddingmatrix 14 defining a common cladding 19. The common cladding 19 can havean outer radius R_(CC), which in the illustrated embodiment of FIGS. 2and 3 corresponds to the outer radius of the coupled-core multicoreoptical fiber 110. A plurality of cores C_(i) (individually denoted C₁and C₂ in the example of FIGS. 2 and 3 and collectively referred to ascores “C”) are disposed within the cladding matrix 14, with each coreC_(i)forming a core fiber CF_(i) that generally extends through a lengthof the coupled-core multicore optical fiber 110 parallel to the centralfiber axis 12. With reference to FIG. 3 , each core C₁ and C₂ includes acentral axis or centerline CL₁ and CL₂ (which define radial position r =0 for each core) and an outer radius r_(C1) and r_(C2), respectively. Aposition of each of the centerlines CL₁ and CL₂ within the coupled-coremulticore optical fiber 110 can be defined using Cartesian coordinateswith the central fiber axis 12 defining the origin (0,0) of an x-ycoordinate system coincident with the coordinate system defined by theradial coordinate R. The position of centerline CL₁ can be defined as(x₁,y₁) and the position of centerline CL₂ can be defined as (x₂,y₂). Adistance D_(C1-C2) between the centerlines CL₁ and CL₂ can then bedefined as √[(x₂- x₁)² + (y₂ - y₁)²], and may be referred to herein as“core pitch.” Thus, for a given core C_(i)having a centerline CL_(i) andan adjacent core C_(j) having a centerline CL_(j), a distance D_(Ci-Cj)is defined as √[(x_(j) - x_(i))² + (y_(j) - y_(i))²]. The plurality ofcores C_(i)may also be spaced apart from the central fiber axis 12 by apredetermined distance D_(12-Ci) as measured from the central fiber axis12 to the centers CL_(i) of each of the plurality of cores C_(i). Theplurality of cores C_(i)may also be spaced apart from the outer surface116 of the coupled-core multicore optical fiber 110 by a predetermineddistance D_(CEi-116) as measured from the edge CE_(i) of each of theplurality of cores C_(i)to the outer surface 116. The D_(CEi-116) may becomposed of a range of values depending on the symmetry of thearrangement of each of the plurality of cores Ci within the coupled-coremulticore optical fiber 110. For instance, the distance between CE₁ andpoint A on outer surface 116 of coupled-core multicore optical fiber 110of FIG. 3 is much smaller than the distance between CE₁ and point B.Without intending to be bound by any particular theory, it is believedthat the extent of signal loss due to tunneling is dependent upon theminimum value for D_(CEi-116).

In embodiments, the multicore optical fiber can have a circularcross-section shape with seven cores, wherein six of the cores are atthe vertices of a hexagon and the seventh core is at the center of thecircular cross-section. In some embodiments, the multicore optical fiberof the present disclosure can have a circular cross-section and thecores can be arranged in a 2 × 2 configuration. In still otherembodiments, the multicore optical fiber of the present disclosure canhave a circular cross-section and the number of cores can be between 10and 20. The coupled-core multicore optical fiber 110 can have N numberof total cores C_(i), wherein i=1 ... N and N is at least 2. Accordingto one aspect of the present disclosure, the total number N of coresC_(i) in the multicore optical fiber 10 is from 2 to 20, 2 to 18, 2 to16, 2 to 12, 2 to 10, 2 to 8, 2 to 6, 2 to 4, 2 to 3, 4 to 20, 4 to 18,4 to 16, 4 to 12, 4 to 10, 4 to 8, 4 to 6, 6 to 20, 6 to 18, 6 to 16, 6to 12, 6 to 10, 6 to 8, 8 to 20, 8 to 18, 8 to 16, 8 to 12, 8 to 10, 10to 20, 10 to 18, 10 to 16, 10 to 12, 12 to 20, 12 to 18, or 12 to 16.For example, the total number N of cores C_(i) in the multicore opticalfiber 10 can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, or any total number N of cores C_(i) between any of thesevalues. The total number N of cores C_(i) can be even or odd and can bearranged in any pattern within the cladding matrix 14, non-limitingexamples of which include a 2 × 2 pattern (or multiples thereof; see,e.g., FIGS. 5A and 5B, discussed below), a square pattern, a rectangularpattern, a circular pattern, and a hexagonal lattice pattern. Forexample, the multicore optical fiber 10 can have N=7 cores C_(i)arranged in a hexagonal lattice pattern. In another example, themulticore optical fiber 10 can have N=12 cores C_(i) arranged in acircular pattern. In one example, the coupled-core multicore opticalfiber 110 can have a core C_(i) positioned such that the core centerlineCL_(i) aligns with the central fiber axis 12. In another example, thecoupled-core multicore optical fiber 110 can have a core C_(i) patternsuch that the cores C_(i) are spaced around the central fiber axis 12.

Referring now to FIG. 4 , according to embodiments, one or more of theplurality of cores C_(i) of the coupled-core multicore optical fiber 110can optionally be surrounded by an inner cladding IC_(i). The innercladding, when included, may help increase coupling and crosstalkbetween adjacent cores. Each inner cladding IC_(i) has an outer radiusr_(ICi) and an inner radius that corresponds to the outer radius rC_(i)of the core C_(i). The inner cladding IC_(i) has a width δr_(ICi)defined by the outer radius rC_(i) of the core C_(i)and the outer radiusr_(ICi) of the inner cladding IC_(i). The core C_(i) can include adiameter d_(i) corresponding to 2*r_(Ci) and the inner cladding IC_(i)can include a diameter d_(IC)i corresponding to 2*r_(ICi). The diameterd_(IC)i also corresponds to the diameter of core fiber CF_(i).

Referring now to FIG. 5A, which depicts an X-Y cross-section of anembodiment of the coupled-core multicore optical fiber 110 in whichcoupled-core multicore optical fiber 110 comprises four cores C₁, C₂,C₃, C₄ disposed in a common cladding. In this embodiment, the commoncladding is an inner common cladding 20 having an outer radius R_(ICC).The inner common cladding 20 surrounds each core of the plurality ofcores (i.e., cores C₁, C₂, C₃, C₄), each core having a radius r_(C1),r_(C2), r_(C3), r_(C4), respectively. The inner common cladding 20 is inturn disposed in an outer common cladding 21 having an outer radiusR_(OOC); the outer radius Rocc also represents the outer radius of theentire glass portion of the coupled-core multicore optical fiber 110.Accordingly, it should be understood that the outer radius R_(ICC) ofthe inner common cladding 20 is less than the radius Rocc of the outercommon cladding 21. It should be understood that what is depicted in thefigures is the “glass portion” of the optical fiber. One or morecoatings may be disposed around the glass portion (i.e., around theouter common cladding 21). The coating(s) may be used to protect theglass of the coupled-core multicore optical fiber 110. Further, thecoating(s) may also be used to enhance the optical properties of thecoupled-core multicore optical fiber 110. Outer common cladding 21 mayhave a radial thickness t_(ROCC) that extends from the outer surface 127of the inner common cladding 20 to the outer surface 116 of thecoupled-core multicore optical fiber 110. The cores C₁, C₂, C₃, C₄ aredistributed within the inner common cladding 20 so as to have a corepitch D_(Ci-Cj). The term “core pitch”, as used herein, refers to thedistance between the centers CL_(i), CL_(j) of two adjacent cores C_(i),C_(j) (i.e., the center-to-center spacing between two adjacent cores).The cores C₁, C₂, C₃, C₄ may also be spaced apart from the central fiberaxis 12 by a predetermined distance D_(12-Ci), where each D_(12-Ci) ismeasured from the central fiber axis 12 to the centers CL₁, CL₂, CL₃,CL₄ of each of the cores C₁, C₂, C₃, C₄, respectively.

In embodiments, the radius R_(ICC) of the inner common cladding 20 maybe greater than or equal to 20 µm and less than or equal to 45 µm orgreater than or equal to 25 µm and less than or equal to 40 µm orgreater than or equal to 20 µm and less than or equal to 30 µm orgreater than or equal to 30 µm and less than or equal to 35 µm or evengreater than or equal to 35 µm and less than or equal to 45 µm. Itshould be understood that the radius R_(ICC) may be within a rangeformed from any one of the lower bounds for the radius R_(ICC) and anyone of the upper bounds of the radius R_(ICC) described herein.

In the same or alternative embodiments, the radius rC_(i) of each coreC_(i)may be greater than or equal to 3 µm and less than or equal to 10µm or greater than or equal to 4 µm and less than or equal to 9 µm orgreater than or equal to 4 µm and less than or equal to 8 µm or greaterthan or equal to 4 µm and less than or equal to 7 µm or greater than orequal to 4 µm and less than or equal to 6 µm or greater than or equal to4 µm and less than or equal to 5 µm or greater than or equal to 5 µm andless than or equal to 7 µm or even greater than or equal to 6 µm andless than or equal to 7 µm. It should be understood that the radiusrC_(i) may be within a range formed from any one of the lower bounds forthe radius rC_(i) and any one of the upper bounds of the radius rC_(i)described herein.

Still referring to FIG. 5A, in embodiments, R_(ICX) may be defined asR_(ICC) - D_(12-Ci)-rC_(i) and is the distance between the edge of coreC_(i) and the edge of the inner common cladding 20 as defined by theradius R_(ICC) along a line formed from the center CL_(i) of the coreand the central fiber axis 12. In embodiments, R_(ICX) may be greaterthan or equal to 15 µm and less than or equal to 30 µm or greater thanor equal to 16 µm and less than or equal to 29 µm or greater than orequal to 17 µm and less than or equal to 28 µm or greater than or equalto 18 µm and less than or equal to 27 µm or greater than or equal to 19µm and less than or equal to 26 µm or greater than or equal to 20 µm andless than or equal to 25 µm or greater than or equal to 21 µm and lessthan or equal to 24 µm or even greater than or equal to 22 µm and lessthan or equal to 23 µm. It should be understood that R_(ICX) may bewithin a range formed from any one of the lower bounds for the radiusR_(ICX) and any one of the upper bounds of the radius R_(ICX) describedherein.

Referring now to FIG. 5B, which depicts an X-Y cross-section of anembodiment of the coupled-core multicore optical fiber 110 in whichcoupled-core multicore optical fiber 110 comprises four cores C₁, C₂,C₃, C₄, each surrounded by an individual inner cladding IC_(i) anddisposed in an outer common cladding 21. Each core of the plurality ofcores (i.e., cores C₁, C₂, C₃, C₄) has radius r_(C1), r_(C2), r_(C3),r_(C4), respectively, and each inner cladding of the plurality of innercladdings has radius r_(ICI), r_(IC2), r_(IC3), r_(IC4), respectively.Each of the plurality of cores is disposed in an outer common cladding21 having an outer radius R_(OOC); the outer radius Rocc also representsthe outer radius of the entire glass portion of the coupled-coremulticore optical fiber 110. It should be understood that what isdepicted in the figures is the “glass portion” of the optical fiber. Oneor more coatings may be disposed around the glass portion (i.e., aroundthe outer common cladding 21). The coating(s) may be used to protect theglass of the coupled-core multicore optical fiber 110. Further, thecoating(s) may also be used to enhance the optical properties of thecoupled-core multicore optical fiber 110. The cores C₁, C₂, C₃, C₄ aredistributed within the common cladding 21 so as to have a core pitchD_(Ci-Cj). The term “core pitch”, as used herein, refers to the distancebetween the centers CL_(i), CL_(j) of two adjacent cores C_(i), C_(j)(i.e., the center-to-center spacing between two adjacent cores). Thecores C₁, C₂, C₃, C₄ may also be spaced apart from the central fiberaxis 12 by a predetermined distance D_(12-Ci), where each D_(12-Ci) ismeasured from the central fiber axis 12 to the centers CL₁, CL₂, CL₃,CL₄ of each of the cores C₁, C₂, C₃, C₄, respectively.

In the same or alternative embodiments, the radius r_(ICi) of each innercladding IC_(i) (depicted in FIG. 4 ) may be greater than or equal to 8µm and less than or equal to 16 µm or greater than or equal to 9 µm andless than or equal to 15 µm or greater than or equal to 10 µm and lessthan or equal to 14 µm or even greater than or equal to 11 µm and lessthan or equal to 13 µm. It should be understood that the radius r_(ICi)may be within a range formed from any one of the lower bounds for theradius r_(ICi) and any one of the upper bounds of the radius r_(ICi)described herein.

While FIGS. 5A and 5B depicts a coupled-core multicore optical fiber 110having four cores CL₁, CL₂, CL₃, CL₄, it should be understood that otherarrangements are contemplated and possible. For example and withoutlimitation, FIGS. 6A-6D show alternative embodiments of coupled-coremulticore optical fiber 110 core layouts with each of the plurality ofcores CL_(i) distributed in the common cladding 21. In particular, FIG.6A shows a coupled-core multicore optical fiber 110a having three coresC₁, C₂, C₃. In this embodiment, the coupled-core multicore optical fiber110a may have a core pitch D_(Ci-Cj) of, for example and withoutlimitation, 38 micrometers (µm). FIG. 6B shows a coupled-core multicoreoptical fiber 110b having three cores C₁, C₂, C₃. In this embodiment,the coupled core multicore optical fiber 110b may have a core pitchD_(Ci-Cj) of, for example and without limitation, 29 µm. FIG. 6C shows acoupled-core multicore optical fiber 110c having six cores C₁, C₂, C₃,C₄, C₅, C₆ arranged in a hexagonal configuration. Hybrid designs withclusters of two or more closely-coupled cores C_(i), C_(j) distributedin the common cladding 21 are also contemplated and possible. Forexample, FIG. 6D shows a coupled-core multicore optical fiber 110dhaving three clusters of three cores C₁, C₂, C₃, C₄, C₅, C₆, C₇, C₈, C₉with each cluster of cores arranged in a triangular configuration. Theembodiment shown in FIG. 6D also includes a tenth marker core, C_(M),which does not transmit data but can facilitate optical alignment of theMCF during splicing and connectorization. It should be understood thatthe foregoing examples are intended to be illustrative, not limiting,and many other arrangements of the cores of the coupled-core multicoreoptical fibers are contemplated and possible.

In embodiments, the core C_(i) may include alkali-doped silica glass,with the inner cladding IC_(i) doped with fluorine to provide an indexdifferential between the core and the common cladding layer. Thealkali-doped silica glass of the core Ci may include for example,concentrations of alkali metal oxide from 20 ppm to 1000 ppm, from 50ppm to 600 ppm, or even from 110 ppm to 200 ppm. The alkali may include,for example, oxides of sodium, potassium, rubidium, lithium, cesium, ora combination of two or more of these. In some embodiments, the corecomprises more than one alkali doped in the core.

In embodiments, the silica-based glass of each of the plurality of coresC_(i) may comprise silica-based glass doped with one or more alkalimetal oxides selected from K₂O, Na₂O, Li20, Cs₂O, Rb₂O, and mixturesthereof. Without intending to be bound by any particular theory, it isbelieved that including alkali metal oxides as dopants in each of theplurality of cores C_(i) may reduce the viscosity of the glass atelevated temperatures which, in turn, aids relaxation by mitigating thedevelopment of stress in the glass during drawing. The mitigation ofstress in the glass decreases the attenuation of the glass. However, ifthe glass is doped with too much alkali, the concentration fluctuationcontribution to Rayleigh scattering may be increased, leading to anincreased observed attenuation. Further, in embodiments in which thesilica-based glass is co-doped with both alkali metal oxides andgermania, undesirable crystallization may occur.

In embodiments including the alkali metal oxide, the concentration ofthe alkali metal oxide in each of the plurality of cores C_(i) may begreater than or equal to 20 ppm and less than or equal to 1000 ppm byweight (0.1 wt.%) of each of the plurality of cores C_(i). For example,the concentration of alkali metal oxide may be greater than or equal to50 ppm (0.005 wt.%) and less than or equal to 950 ppm (0.095 wt.%) orgreater than or equal to 100 ppm (0.01 wt.%) and less than or equal to900 ppm (0.09 wt.%) or greater than or equal to 150 ppm (0.015 wt.%) andless than or equal to 850 ppm (0.085 wt.%) or greater than or equal to200 ppm (0.02 wt.%) and less than or equal to 800 ppm (0.08 wt.%) orgreater than or equal to 250 ppm (0.025 wt.%) and less than or equal to750 ppm (0.075 wt.%) or greater than or equal to 300 ppm (0.03 wt.%) andless than or equal to 700 ppm (0.07 wt.%) or greater than or equal to350 ppm (0.035 wt.%) and less than or equal to 650 ppm (0.065 wt.%) orgreater than or equal to 400 ppm (0.04 wt.%) and less than or equal to600 ppm (0.06 wt.%) or even greater than or equal to 450 ppm (0.045wt.%) and less than or equal to 550 ppm (0.055 wt.%). It should beunderstood that the amount of alkali metal oxide in the silica-basedglass may be within a range formed from any one of the lower bounds foralkali metal oxide and any one of the upper bounds of alkali metal oxidedescribed herein.

In the same or different embodiments, the silica-based glass of each ofthe plurality of cores C_(i) may comprise silica-based glass doped withfluorine. Fluorine is a down-dopant that reduces the index of refractionof each of the plurality of cores C_(i) relative to undoped silica. Insome embodiments, the concentration of fluorine in each of the pluralityof cores C_(i) is greater than or equal to 0.02 wt.% and less than orequal to 0.15 wt.% by weight of the fully formed core C_(i). Forexample, the concentration of fluorine in each of the plurality of coresC_(i) may be greater than or equal to 0.04 wt.% and less than or equalto 0.13 wt.%, greater than or equal to 0.06 wt.% and less than or equalto 0.11 wt.%, or even greater than or equal to 0.08 wt.% and less thanor equal to 0.09 wt.%. It should be understood that the amount offluorine in the compositions may be within a range formed from any oneof the lower bounds for fluorine and any one of the upper bounds offluorine described herein.

In embodiments, the silica-based glass of each of the plurality of coresC_(i) may comprise silica-based glass doped with chlorine. Chlorine isan up-dopant that increases the index of refraction of each of theplurality of cores C_(i) relative to undoped silica. In someembodiments, the concentration of the chlorine in each of the pluralityof cores C_(i) is greater than or equal to 1 wt.% and less than or equalto 7 wt.% by weight of each of the plurality of cores C_(i). Forexample, the concentration of chlorine may be greater than or equal to1.5 wt.% and less than or equal to 7 wt.%, greater than or equal to 2wt.% and less than or equal to 6.5 wt.%, greater than or equal to 2.5wt.% and less than or equal to 6 wt.%, greater than or equal to 3 wt.%and less than or equal to 5.5 wt.%, greater than or equal to 3.5 wt.%and less than or equal to 5 wt.%, or even greater than or equal to 4wt.% and less than or equal to 4.5 wt.%. It should be understood thatthe amount of chlorine in the compositions may be within a range formedfrom any one of the lower bounds for chlorine and any one of the upperbounds of chlorine described herein.

In embodiments, the silica-based glass of each of the plurality of coresC_(i) may comprise silica-based glass doped with phosphorus. Phosphorusis an up-dopant that increases the index of refraction of each of theplurality of cores C_(i) relative to undoped silica. In embodiments inwhich the phosphorus is present, the concentration of phosphorus in eachof the plurality of cores C_(i) is greater than 0 wt.% and less than orequal to 2 wt.% or greater than or equal to 0.2 wt.% and less than orequal to 1.8 wt.% or greater than or equal to 0.4 wt.% and less than orequal to 1.6 wt.% or greater than or equal to 0.6 wt.% and less than orequal to 1.4 wt.% or greater than or equal to 0.8 wt.% and less than orequal to 1.2 wt.% or even greater than or equal to 1 wt.% and less thanor equal to 1.1 wt.%. It should be understood that the amount ofphosphorus in the compositions may be within a range formed from any oneof the lower bounds for phosphorus and any one of the upper bounds ofphosphorus described herein.

In embodiments, the silica-based glass of each of the plurality of coresC_(i) may comprise silica-based glass doped with phosphorus and one ormore alkali metal oxides. In embodiments, the silica-based glass of eachof the plurality of cores C_(i) may comprise silica-based glass dopedwith phosphorus and chlorine. In embodiments in which both phosphorusand chlorine are present, the concentration of chlorine may be greaterthan or equal to 1 wt.% to less than or equal to 6.5 wt.%, and theconcentration of phosphorus may be greater than or equal to 0.5 wt.% andless than or equal to 2 wt.%. For example, the concentration of chlorinemay be greater than or equal to 1.5 wt.% and less than or equal to 6wt.% or greater than or equal to 2 wt.% and less than or equal to 5.5wt.% or greater than or equal to 2.5 wt.% and less than or equal to 5wt.% or greater than or equal to 3 wt.% and less than or equal to 4.5wt.% or even greater than or equal to 3.5 wt.% and less than or equal to4 wt.%. It should be understood that the amount of chlorine in thecompositions may be within a range formed from any one of the lowerbounds for chlorine and any one of the upper bounds of chlorinedescribed herein. Further, the concentration of phosphorus may begreater than or equal to 0.6 wt.% and less than or equal to 1.9 wt.% orgreater than or equal to 0.7 wt.% and less than or equal to 1.8 wt.% orgreater than or equal to 0.8 wt.% and less than or equal to 1.7 wt.% orgreater than or equal to 0.9 wt.% and less than or equal to 1.6 wt.% orgreater than or equal to 1 wt.% and less than or equal to 1.5 wt.% orgreater than or equal to 1.1 wt.% and less than or equal to 1.4 wt.% oreven greater than or equal to 1.2 wt.% and less than or equal to 1.3wt.%. It should be understood that the amount of phosphorus in thecompositions may be within a range formed from any one of the lowerbounds for phosphorus and any one of the upper bounds of phosphorusdescribed herein.

When present, the inner common cladding 20 may comprise silica-basedglass. In embodiments, the inner common cladding 20 may consist of, orconsist essentially of, silica-based glass. In embodiments, thesilica-based glass of the inner common cladding 20 may comprise adown-dopant such that the inner common cladding 20 has an index ofrefraction lower than that of each of the plurality of cores Ci. Inembodiments, the down-dopant is fluorine.

In some embodiments, inner common cladding 20, when present, may includefluorine in a concentration greater than or equal to 0.5 wt.% and lessthan or equal to 1.8 wt.%. For example, the inner common cladding 20 mayinclude fluorine in a concentration greater than or equal to 0.6 wt.%and less than or equal to 1.7 wt.% or greater than or equal to 0.7 wt.%and less than or equal to 1.6 wt.% or greater than or equal to 0.8 wt.%and less than or equal to 1.5 wt.% or greater than or equal to 0.9 wt.%and less than or equal to 1.4 wt.% or greater than or equal to 1 wt.%and less than or equal to 1.3 wt. % or even greater than or equal to 1.1wt. % and less than or equal to 1.2 wt.% It should be understood thatthe amount of fluorine in the compositions may be within a range formedfrom any one of the lower bounds for fluorine and any one of the upperbounds of fluorine described herein.

The outer common cladding 21 may comprise silica-based glass. Inembodiments, the outer common cladding 21 may consist of, or consistessentially of, silica-based glass. In embodiments, the silica-basedglass of the outer common cladding 21 may comprise a down-dopant, suchas fluorine, which reduces the index of refraction such that the outercommon cladding 21 has an index of refraction lower than that of each ofthe plurality of cores C₁ and higher than that of the inner commoncladding 20. In other embodiments, each of the plurality of cores C₁ maybe undoped, the inner common cladding 20 may include a down-dopant, andthe outer common cladding may include an up-dopant. Exemplary up-dopantsinclude, but are not limited to, chlorine, germania, and titania.

In some embodiments, the concentration of fluorine in the silica-basedglass of the outer common cladding 21 is greater than or equal to 0.3wt.% and less than or equal to 1.6 wt.% of the fully formed outer commoncladding 21. For example, the concentration of fluorine may be greaterthan or equal to 0.4 wt.% and less than or equal to 1.5 wt.% or greaterthan or equal to 0.7 wt.% and less than or equal to 1.4 wt.% or greaterthan or equal to 0.8 wt.% and less than or equal to 1.3 wt.% or greaterthan or equal to 0.9 wt.% and less than or equal to 1.2 wt.% or evengreater than or equal to 1 wt.% and less than or equal to 1.1 wt.%. Itshould be understood that the amount of fluorine in the compositions maybe within a range formed from any one of the lower bounds for fluorineand any one of the upper bounds of fluorine described herein.

Still referring to FIGS. 5A-5B and 6A-6D, to facilitate coupling betweeneach of the plurality of cores C₁ of the coupled-core multicore opticalfiber 110, the core pitch D_(Ci-cj) may be greater than or equal to 20µm and less than or equal to 40 µm. For example, the core pitch D_(Ci-)_(Cj) may be greater than or equal to 20 µm and less than or equal to 35µm, greater than or equal to 22 µm and less than or equal to 32 µm,greater than or equal to 24 µm and less than or equal to 30 µm, greaterthan or equal to 25 µm and less than or equal to 30 µm, greater than orequal to 20 µm and less than or equal to 28 µm, greater than or equal to20 µm and less than or equal to 26 µm, greater than or equal to 30 µmand less than or equal to 40 µm, or even greater than or equal to 32 µmand less than or equal to 38 µm. It should be understood that the corepitch D_(ci-cj) may be within a range formed from any one of the lowerbounds for core pitch D_(Ci-Cj) and any one of the upper bounds of corepitch D_(Ci-Cj) described herein.

To minimize radiation or tunneling loss, the minimum distance D_(Ci-116)from the centers CL_(i) of each of the plurality of cores C_(i) to theouter surface 116 of the coupled-core multicore optical fiber 110 may begreater than or equal to 30 µm in a plane perpendicular to the long axisof the coupled-core multicore optical fiber (i.e., the X-Y plane of thecoordinate axes depicted in the figures), such as greater than or equalto 30 µm and less than or equal to 50 µm. For example, the distanceD_(Ci-116) may be greater than or equal to 32 µm and less than or equalto 48 µm, greater than or equal to 34 µm and less than or equal to 46µm, greater than or equal to 34 µm and less than or equal to 44 µm,greater than or equal to 36 µm and less than or equal to 42 µm, greaterthan or equal to 30 µm and less than or equal to 40 µm, greater than orequal to 32 µm and less than or equal to 38 µm, greater than or equal to34 µm and less than or equal to 36 µm, greater than or equal to 40 µmand less than or equal to 50 µm, greater than or equal to 42 µm and lessthan or equal to 48 µm, or even greater than or equal to 44 µm and lessthan or equal to 46 µm. It should be understood that the distanceD_(Ci-116) may be within a range formed from any one of the lower boundsfor this distance D_(Ci-116) and any one of the upper bounds of thisdistance D_(Ci-) 116 described herein.

Referring to FIGS. 7A, 7B, and 8 , various properties of the innercommon cladding 20, the outer common cladding 21, and each of theplurality of cores C_(i) and inner claddings IC_(i) will be described inmore detail. Some properties are discussed with reference to an“individual core,” C_(i), and are applicable to any of the plurality ofcores C_(i). Other properties characterize a relationship between atleast two cores C_(i) and C_(j). For ease of explanation andunderstanding, the first core C₁ and the second core C₂ are used inthese descriptions. However, it should be understood that theseproperties may apply to any two cores of the plurality of cores C_(i).

FIG. 7A shows a relative refractive index profile of a portion of anoptical fiber preform from which a coupled-core multicore optical fibermay be drawn, such as the coupled-core multicore optical fiber depictedin FIG. 5A, according to embodiments. The relative refractive indexprofile of FIG. 7A is presented herein to illustrate the relativepositioning of portions of a single core of the coupled-core multicoreoptical fiber as well as the relative refractive index of a single coreof the coupled-core optical fiber. The dimensions of the Y axis and theX axis have been omitted and the variables (such as r_(CL1), r_(C1),R_(ICX), etc.) are superimposed on the ordinates for purposes ofillustration only. The horizontal axis of FIG. 7A generally correspondsto the coupled-core multicore optical fiber along a path from a centerline CL_(i) of a core C_(i) through inner common cladding 20, and acrossouter common cladding 21, with center line CL₁ representing the r = 0value of the horizontal axis and Radius referring to radial coordinater. The vertical axis corresponds to the relative refractive index Δ%(Delta%) as a function of the dimension of the coupled-core multicoreoptical fiber along the path. At center line CL₁, the core has arelative refractive index Δ_(CLI), relative to pure silica, and thecenterline region extends to radius r_(CL1.) The core C₁ surrounds thecenterline region and has a radius r_(Cl) with average relativerefractive index Δ_(CI), relative to pure silica. Between the edge(r_(C1)) of the core C_(l) and the edge of the inner common cladding ICCof the coupled-core multicore optical fiber 110, designated as R_(ICX,)the inner common cladding ICC has an average relative refractive indexΔ_(ICC,) relative to pure silica. In the embodiment shown in FIG. 7A,the inner common cladding ICC is surrounded by outer common claddingOCC, which has an average relative refractive index Δ_(OCC,) relative topure silica. In embodiments, Δ_(CLI) > Δ_(Cl) > Δ_(ICC). In embodiments,Δ_(CLI) > Δ_(Cl) > Δ_(occ) > Δ_(ICC.) In embodiments, without theoptional higher index inner core segment, Δ_(Cl) > Δ_(ICC). In some ofthese embodiments, Δ_(Cl) > Δ_(OCC) > Δ_(ICC.) The dopants may be used,as described in the preceding paragraphs, to achieve the desireddifferences in A_(CL1,) Δ_(CI), and Δ_(ICC).

FIG. 7B shows a relative refractive index profile of a portion of anoptical fiber preform from which a coupled-core multicore optical fibermay be drawn, such as the coupled-core multicore optical fiber depictedin FIG. 5B, according to embodiments. The relative refractive indexprofile of FIG. 7B is presented herein to illustrate the relativepositioning of portions of a single core of the coupled-core multicoreoptical fiber as well as the relative refractive index of a single coreof the coupled-core optical fiber. The dimensions of the Y axis and theX axis have been omitted and the variables (such as r_(CL1), r_(C1),R_(ICI), etc.) are superimposed on the ordinates for purposes ofillustration only. The horizontal axis of FIG. 7B generally correspondsto the coupled-core multicore optical fiber along a path from a centerline CL_(i) of a core C_(i) through inner cladding IC, and across outercommon cladding 21, with center line CL₁ representing the r = 0 value ofthe horizontal axis and Radius referring to radial coordinate r. Thevertical axis corresponds to the relative refractive index Δ% (Delta%)as a function of the dimension of the coupled-core multicore opticalfiber along the path. At center line CL₁, the core has a relativerefractive index Δ_(CLI,) relative to pure silica, and the centerlineregion extends to radius r_(CL1.) The core C₁ surrounds the centerlineregion and has a radius r_(Cl) with average relative refractive indexΔ_(CI), relative to pure silica. Between the edge (r_(C1)) of the coreC_(i) and the edge of the inner cladding IC_(i) of the coupled-coremulticore optical fiber 110, designated as R_(ICI), the inner claddingIC_(i) has an average relative refractive index Δ_(ICI), relative topure silica. In the embodiment shown in FIG. 7B, the inner claddingIC_(i) is surrounded by outer common cladding OCC, which has an averagerelative refractive index ΔOCC, relative to pure silica. In embodiments,Δ_(CLI) > Δ_(Cl) > Δ_(ICI). In embodiments, Δ_(CLI) > Δ_(Cl) > Δ_(OCC) >Δ_(ICI). In embodiments, without the optional higher index inner coresegment, Δ_(Cl) > Δ_(ICI). In some of these embodiments, Δ_(C1) >Δ_(OCC) > Δ_(IC1). The dopants may be used, as described in thepreceding paragraphs, to achieve the desired differences in Δ_(CL1,)Δ_(C1), and Δ_(IC1).

In embodiments, Δ_(CLI) is greater than or equal to -0.1 Δ% and lessthan or equal to 0.3 Δ%. For example, Δ_(CLI) may be greater than orequal to -0.05 Δ% and less than or equal to 0.25 Δ% or greater than orequal to -0.03 Δ% and less than or equal to 0.2 Δ% or even greater thanor equal to -0.03 Δ% and less than or equal to 0.15 Δ%. It should beunderstood Δ_(CLI) may be within a range formed from any one of thelower bounds for Δ_(CL1) and any one of the upper bounds of Δ_(CL1)described herein.

In embodiments, Δ_(Cl) is greater than or equal to -0.1 Δ% and less thanor equal to 0.2 Δ%. For example, Δ_(Cl) may be greater than or equal to-0.05 Δ% and less than or equal to 0.15 Δ% or even greater than or equalto 0 Δ% and less than or equal to 0.1 Δ%. It should be understood Δ_(Cl)may be within a range formed from any one of the lower bounds for Δ_(Cl)and any one of the upper bounds of Δ_(Cl) described herein.

In embodiments with an inner common cladding as depicted in FIG. 5A,Δ_(ICC) is greater than or equal to -0.4 Δ% and less than or equal to-0.2 Δ%. For example, Δ_(ICC) may be greater than or equal to -0.35 Δ%and less than or equal to -0.25 Δ%. It should be understood Δ_(ICC) maybe within a range formed from any one of the lower bounds for Δ_(ICC)and any one of the upper bounds of Δ_(ICC) described herein.

In embodiments in which each of the plurality of the cores is surroundedby an individual inner cladding as depicted in FIG. 5B, Δ_(ICI) isgreater than or equal to -0.4 Δ% and less than or equal to -0.2 Δ%. Forexample, Δ_(ICI) may be greater than or equal to -0.35 Δ% and less thanor equal to -0.25 Δ%. It should be understood Δ_(IC1) may be within arange formed from any one of the lower bounds for Δ_(ICI) and any one ofthe upper bounds of Δ_(ICI) described herein.

In embodiments, Δ_(OCC) is greater than or equal to -0.4 Δ% and lessthan or equal to -0.2 Δ%. For example, Δ_(OCC) may be greater than orequal to -0.35 Δ% and less than or equal to -0.25 Δ%. It should beunderstood Δ_(OCC) may be within a range formed from any one of thelower bounds for Δ_(OCC) and any one of the upper bounds of Δ_(OCC)described herein.

While not intending to be limited by theory, the electro-magnetic fieldsof the waves (e.g., light waves) propagating in the coupled-coremulticore optical fiber 110 may be coupled, for example, selectivelycoupled, when certain conditions are met. For example, each of theplurality of cores C_(i) of the coupled-core multicore optical fiber 110may be characterized by a plurality of coupling coefficients (i.e.,various coupling coefficients for coupling from one individual core,such as the first core C₁, to another individual core, such as thesecond core C₂). Coupling coefficients measure the amount of overlaybetween the modal fields of two cores of the plurality of cores C₁, suchas the first core C₁ and the second core C₂. Modal fields of the coresdepend on various parameters, such as the radius of the core r_(Ci), therefractive index of the core, the material of the core, the material ofthe cladding, and the wavelength of operation (λ) (i.e., the wavelengthof light propagating in the core).

The coupling coefficient κ between two adjacent cores C_(1,) C₂ dependupon the core pitch between adjacent cores, which may also be referredto as the core spacing. Larger coupling coefficients are expected as thedistance between cores decreases. For instance, at very small corespacing, e.g. 15 µm, the coupling coefficient may be greater than orequal to 100 (linear units) per meter and less than or equal to 600 permeter, or greater than or equal to 150 per meter and less than or equalto 550 per meter, or even greater than or equal to 300 per meter andless than or equal to 400 per meter. However, at very large corespacing, e.g. 60 µm, the coupling coefficient may be greater than orequal to 8 × 10⁻⁶ per meter and less than or equal to 4 × 10⁻⁴ permeter.

In embodiments, the coupling coefficient may be greater than or equal to1 × 10⁻³ /m. For instance, the power coupling coefficient may be greaterthan or equal to 1 × 10⁻³ /m and less than or equal to 5 × 10⁻³ /m orgreater than or equal to 1.5 × 10⁻³ /m and less than or equal to 4.5 ×10⁻³ /m or greater than or equal to 2 × 10⁻³ /m and less than or equalto 4 × 10⁻³ /m or even greater than or equal to 2.5 × 10⁻³ /m and lessthan or equal to 3.5 × 10⁻³ /m.

Another parameter affecting the transmission of information using thefibers described herein is crosstalk. In various embodiments, thecrosstalk between two adjacent cores 120a, 120b is greater than or equalto -30 dB for 1 km fiber length and less than or equal to 0 dB for 1 kmfiber length. For example, the crosstalk may be greater than or equal to-25 dB for 1 km fiber length and less than or equal to -1 dB for 1 kmfiber length, greater than or equal to -20 dB for 1 km fiber length andless than or equal to -2 dB for 1 km fiber length, greater than or equalto -15 dB for 1 km fiber length and less than or equal to -3 dB for 1 kmfiber length, or even greater than or equal to -10 dB for 1 km fiberlength and less than or equal to -4 dB for 1 km fiber length. It shouldbe understood crosstalk may be within a range formed from any one of thelower bounds for crosstalk and any one of the upper bounds of crosstalkdescribed herein.

In embodiments, each core of the coupled-core multicore optical fiber110 may have an effective area A_(eff) of greater than 100 µm² at awavelength of 1550 nm. The effective area is determined individually foreach core of the coupled-core multicore optical fiber withoutconsideration of the effects of crosstalk between the cores of thecoupled-core multicore optical fiber. For instance, the effective areaor each core may be greater than or equal to 110 µm² and less than orequal to 160 µm², greater than or equal to 120 µm² and less than orequal to 158 µm², greater than or equal to 124 µm² and less than orequal to 156 µm², greater than or equal to 126 µm² and less than orequal to 154 µm², greater than or equal to 128 µm² and less than orequal to 152 µm², greater than or equal to 130 µm² and less than orequal to 150 µm², greater than or equal to 132 µm² and less than orequal to 148 µm², greater than or equal to 134 µm² and less than orequal to 146 µm², greater than or equal to 136 µm² and less than orequal to 144 µm², or even greater than or equal to 138 µm² and less thanor equal to 142 µm². In other embodiments, each core of the coupled-coremulticore optical fiber 110 may have an effective area of greater thanor equal to 70 µm² and less than or equal to 85 µm² at a wavelength of1550 nm. For instance, the effective area of each core may be greaterthan or equal to 71 µm² and less than or equal to 84 µm², greater thanor equal to 72 µm² and less than or equal to 83 µm², greater than orequal to 73 µm² and less than or equal to 82 µm², greater than or equalto 74 µm² and less than or equal to 81 µm², greater than or equal to 75µm² and less than or equal to 80 µm², greater than or equal to 76 µm²and less than or equal to 79 µm², or even greater than or equal to 77µm² and less than or equal to 78 µm². It should be understood that theA_(eff) of each core of the coupled-core multicore optical fiber 110 maybe within a range formed from any one of the lower bounds for A_(eff)and any one of the upper bounds of A_(eff) described herein.

The average attenuation of the coupled-core multicore optical fiber isdetermined by measuring the attenuation for each core of thecoupled-core multicore optical fiber at a wavelength of 1510 nm and thencalculating an average attenuation for the entire coupled-core multicoreoptical fiber based on the individual attenuation measurements of eachcore. In embodiments, the average attenuation of the coupled-coremulticore optical fiber 110 is less than or equal to 0.18 dB/km, lessthan or equal to 0.175 dB/km, less than or equal to 0.17 dB/km, or evenless than or equal to 0.165 dB/km. In embodiments, the attenuation ofthe optical fiber at a wavelength of 1550 nm may be greater than orequal to 0.16 dB/km and less than or equal to 0.18 dB/km, greater thanor equal to 0.165 dB/km and less than or equal to 0.175 dB/km, greaterthan or equal to 0.16 dB/km and less than or equal to 0.175 dB/km, oreven greater than or equal to 0.165 dB/km and less than or equal to 0.18dB/km. It should be understood that the attenuation of the coupled-coremulticore optical fiber 110 may be within a range formed from any one ofthe lower bounds for attenuation and any one of the upper bounds ofattenuation described herein.

In various embodiments, the cable cutoff of each core of thecoupled-core multicore optical fiber 110 is greater than or equal to1200 nm and less than or equal to 1530 nm. For example, the cable cutoffof each core of each core of the coupled-core multicore optical fiber110 may be greater than or equal to 1220 nm and less than or equal to1530 nm, greater than or equal to 1240 nm and less than or equal to 1530nm, greater than or equal to 1260 nm and less than or equal to 1530 nm,greater than or equal to 1280 nm and less than or equal to 1530 nm,greater than or equal to 1300 nm and less than or equal to 1500 nm,greater than or equal to 1320 nm and less than or equal to 1480 nm,greater than or equal to 1340 nm and less than or equal to 1460 nm,greater than or equal to 1360 nm and less than or equal to 1440 nm,greater than or equal to 1380 nm and less than or equal to 1420 nm,greater than or equal to 1390 nm and less than or equal to 1400 nm,greater than or equal to 1300 and less than or equal to 1500 nm, or evengreater than or equal to 1320 and less than or equal to 1480 nm. Itshould be understood that the cable cutoff of each core of thecoupled-core multicore optical fiber 110 may be within a range formedfrom any one of the lower bounds for cable cutoff and any one of theupper bounds of cable cutoff described herein.

The average 15 mm bend loss of the coupled-core multicore optical fiberis determined by measuring the 15 mm bend loss for each core of thecoupled-core multicore optical fiber at a wavelength of 1510 nm and thencalculating an average 15 mm bend loss for the entire coupled-coremulticore optical fiber based on the individual 15 mm bend lossmeasurements of each core. In various embodiments, the average bend lossof the coupled-core multicore optical fiber 110 measured at a wavelengthof 1550 nm using a mandrel with a 15 mm diameter (“1 × 15 mm diameterbend loss”) is greater than or equal to 0.1 dB/turn and less than orequal to 10 dB/turn. For example, the 1 × 15 mm diameter bend loss at 15mm is less than or equal to 5 dB/turn, less than or equal to 4 dB/turn,less than or equal to 3 dB/turn, less than or equal to 2 dB/turn, oreven less than or equal to 1 dB/turn.

The average 20 mm bend loss of the coupled-core multicore optical fiberis determined by measuring the 20 mm bend loss for each core of thecoupled-core multicore optical fiber at a wavelength of 1510 nm and thencalculating an average 20 mm bend loss for the entire coupled-coremulticore optical fiber based on the individual 20 mm bend lossmeasurements of each core. In various embodiments, the average bend lossof the coupled-core multicore optical fiber 110 at a wavelength of 1550nm using a mandrel with a 20 mm diameter (“1 × 20 bend loss”) is greaterthan or equal to 0.01 dB/turn and less than or equal to 1 dB/turn. Forexample, the 1 x 20 bend loss is less than or equal to 0.8 dB/turn, lessthan or equal to 0.6 dB/turn, less than or equal to 0.5 dB/turn, lessthan or equal to 0.4 dB/turn, less than or equal to 0.3 dB/turn, or evenless than or equal to 0.2 dB/turn.

The average 30 mm bend loss of the coupled-core multicore optical fiberis determined by measuring the 30 mm bend loss for each core of thecoupled-core multicore optical fiber at a wavelength of 1510 nm and thencalculating an average 30 mm bend loss for the entire coupled-coremulticore optical fiber based on the individual 30 mm bend lossmeasurements of each core. In various embodiments, the average bend lossat 1550 nm of the coupled-core multicore optical fiber 110 at awavelength of 1550 nm using a mandrel with a 30 mm diameter (“1 × 30bend loss”) is greater than or equal to 0.001 dB/turn and less than orequal to 0.03 dB/turn. For example, the 1 × 30 bend loss is greater thanor equal to 0.001 dB/turn and less than or equal to 0.025 dB/turn oreven greater than or equal to 0.001 dB/turn and less than or equal to0.02 dB/turn. It should be understood that the 1 × 30 bend loss mm ofthe coupled-core multicore optical fiber 110 may be within a rangeformed from any one of the lower bounds for 1 × 30 bend loss and any oneof the upper bounds of 1 × 30 bend loss described herein.

In various embodiments, the zero-dispersion wavelength of each core ofthe coupled-core multicore optical fiber 110 is greater than or equal to1200 nm and less than or equal to 1350 nm. For example, thezero-dispersion wavelength of each core of the coupled-core multicoreoptical fiber 110 may be greater than or equal to 1225 nm and less thanor equal to 1325 nm or even greater than or equal to 1250 nm and lessthan or equal to 1300 nm. It should be understood that thezero-dispersion wavelength of each core of the coupled-core multicoreoptical fiber 110 may be within a range formed from any one of the lowerbounds for zero-dispersion wavelength and any one of the upper bounds ofzero-dispersion wavelength described herein.

In various embodiments, dispersion at 1310 nm of each core of thecoupled-core multicore optical fiber 110 is greater than or equal to 0.2ps/nm/km and less than or equal to 3.5 ps/nm/km. For example, thedispersion at 1310 of each core of the coupled-core multicore opticalfiber 110 may be greater than or equal to 0.5 ps/nm/km and less than orequal to 3 ps/nm/km, greater than or equal to 1 ps/nm/km and less thanor equal to 2.5 ps/nm/km, or even greater than or equal to 1.5 ps/nm/kmand less than or equal to 2 ps/nm/km. It should be understood that thedispersion at 1310 nm of each core of the coupled-core multicore opticalfiber 110 may be within a range formed from any one of the lower boundsfor dispersion at 1310 nm and any one of the upper bounds of dispersionat 1310 nm described herein.

In various embodiments, the dispersion slope at 1310 nm of each core ofthe coupled-core multicore optical fiber 110 is greater than or equal to0.08 ps/nm²/km and less than or equal to 0.095 ps/nm²/km. For example,the dispersion slope at 1310 nm of each core of the coupled-coremulticore optical fiber 110 may be greater than or equal to 0.081ps/nm²/km and less than or equal to 0.094 ps/nm²/km, greater than orequal to 0.082 ps/nm²/km and less than or equal to 0.093 ps/nm²/km,greater than or equal to 0.083 ps/nm²/km and less than or equal to 0.092ps/nm²/km, greater than or equal to 0.084 ps/nm²/km and less than orequal to 0.091 ps/nm²/km, greater than or equal to 0.085 ps/nm²/km andless than or equal to 0.09 ps/nm²/km, greater than or equal to 0.086ps/nm²/km and less than or equal to 0.089 ps/nm²/km, or even greaterthan or equal to 0.087 ps/nm²/km and less than or equal to 0.088ps/nm²/km. It should be understood that the dispersion slope at 1310 nmof each core of the coupled-core multicore optical fiber 110 may bewithin a range formed from any one of the lower bounds for dispersionslope at 1310 nm and any one of the upper bounds of dispersion slope at1310 nm described herein.

In various embodiments, dispersion at 1550 nm of each core of thecoupled-core multicore optical fiber 110 is greater than or equal to 15ps/nm/km and less than or equal to 25 ps/nm/km. For example, dispersionat 1550 of each core of the coupled-core multicore optical fiber 110 maybe greater than or equal to 16 ps/nm/km and less than or equal to 24ps/nm/km, greater than or equal to 17 ps/nm/km and less than or equal to23 ps/nm/km, greater than or equal to 18 ps/nm/km and less than or equalto 22 ps/nm/km, or even greater than or equal to 19 ps/nm/km and lessthan or equal to 21 ps/nm/km. It should be understood that thedispersion at 1550 nm of each core of the coupled-core multicore opticalfiber 110 may be within a range formed from any one of the lower boundsfor dispersion at 1550 nm and any one of the upper bounds of dispersionat 1550 nm described herein.

In various embodiments, the dispersion slope at 1550 nm of each core ofthe coupled-core multicore optical fiber 110 is greater than or equal to0.05 ps/nm²/km and less than or equal to 0.065 ps/nm²/km. For example,the dispersion slope at 1550 nm of each core of the coupled-coremulticore optical fiber 110 may be greater than or equal to 0.051ps/nm²/km and less than or equal to 0.064 ps/nm²/km, greater than orequal to 0.052 ps/nm²/km and less than or equal to 0.063 ps/nm²/km,greater than or equal to 0.053 ps/nm²/km and less than or equal to 0.062ps/nm²/km, greater than or equal to 0.054 ps/nm²/km and less than orequal to 0.061 ps/nm²/km, greater than or equal to 0.055 ps/nm²/km andless than or equal to 0.06 ps/nm²/km, greater than or equal to 0.056ps/nm²/km and less than or equal to 0.059 ps/nm²/km, or even greaterthan or equal to 0.057 ps/nm²/km and less than or equal to 0.058ps/nm²/km. It should be understood that the dispersion slope at 1550 nmof each core of the coupled-core multicore optical fiber 110 may bewithin a range formed from any one of the lower bounds for dispersionslope at 1550 nm and any one of the upper bounds of dispersion slope at1550 nm described herein.

The coupled-core multicore optical fiber 110 of the present disclosurecan be made using any suitable method for forming a multicore opticalfiber. See, for example, U.S. Pat. No. 9,120,693 and U.S. Published Pat.Application No. 20150284286, the disclosures of which are incorporatedherein by reference in their entirety. For example, the coupled-coremulticore optical fiber 110 can be formed by drawing a multicore preformmade using conventional optical-fiber techniques, such as glass drillingor stacking. The glass drilling method can be used to form a multicorepreform by drilling holes in a silica glass cylinder (pure, undopedsilica or doped silica). The locations and dimensions of the holes arebased on the multicore optical fiber design. Core canes having thedesired refractive index profile and a diameter that is slightly smallerthan the pre-drilled holes are then inserted into the pre-drilled holesto form the multicore preform. The multicore preform is then heated to atemperature sufficient to melt the silica glass forming the pre-drilledholes such that the pre-drilled holes collapse around the core canes.The multicore preform is then drawn into a fiber. The core canes can bemade using any suitable conventional preform manufacturing technique,such as outside vapor deposition (OVD), modified chemical vapordeposition (MCVD), or plasma activated chemical vapor deposition (PCVD).

Suitable precursors for silica include SiCl₄ and organosiliconcompounds. Organosilicon compounds are silicon compounds that includecarbon, and optionally oxygen and/or hydrogen. Examples of suitableorganosilicon compounds include octamethylcyclotetrasiloxane (OMCTS),silicon alkoxides (Si(OR)₄), organosilanes (SiR₄), andSi(OR)_(x)R_(4-x), where R is a carbon-containing organic group orhydrogen and where R may be the same or different at each occurrence,and wherein at least one R is a carbon-containing organic group.Suitable precursors for chlorine doping include Cl₂, SiCl₄, Si₂Cl₆,Si₂OCl₆, SiCl₃H, and CCl₄. Suitable precursors for fluorine dopinginclude F₂, CF₄, and SiF₄. Regions of constant refractive index may beformed by not doping or by doping at a uniform concentration over thethickness of the region. Regions of variable refractive index are formedthrough non-uniform spatial distributions of dopants over the thicknessof a region and/or through incorporation of different dopants indifferent regions. The OVD, MCVD, PCVD and other techniques forgenerating silica soot permit fine control of dopant concentrationthrough layer-by-layer deposition with variable flow rate delivery ofdopant precursors.

One exemplary method that can be used to form the multicore opticalfibers of the present disclosure is a method that utilizes a cane-basedoptical fiber preform and then draws the optical fiber from thecane-based glass preform. An exemplary cane-based glass preform methodis disclosed in Applicant’s co-pending U.S. Pat. Application Serial No.62/811,842 (Attorney Docket No. SP19-067PZ), entitled “Vacuum-BasedMethods of Forming a Cane-Based Optical Fiber Preform and Methods ofForming an Optical Fiber Using Same,” which was filed on Feb. 28, 2019,the contents of which are incorporated herein by reference in theirentirety.

Briefly, a cane-based glass preform method for forming the multicoreoptical fibers 10 can include utilizing one or more glass claddingsections each having one or more precision axial holes formed thereinand a top end with a recess defined by a perimeter lip. When usingmultiple glass cladding sections, the sections can be stacked so thatthe axial holes are aligned. A core cane can then be added to each axialhole to define a cane-cladding assembly. Top and bottom caps,respectively, can be added to the top and bottom of the cane-claddingassembly to define a preform assembly. The top cap closes off the recessat the top of the glass-cladding section. The bottom cap can have itsown raised lip and recess that becomes closed off when the bottom cap isinterfaced with the bottom end of the cane-cladding assembly. Theclosed-off recesses and gaps formed by the canes within the axial holesdefine a substantially sealed internal chamber. The preform assembly canthen be dried and purified by drawing a select cleaning gas (e.g.,chlorine) through a small passage in the bottom cap that leads to theinternal chamber. A vacuum can be applied through the top cap to createa pressure differential between the internal chamber and the ambientenvironment. The pressure differential facilitates maintaining thecomponents of the preform assembly together, and can be referred to as avacuum-held preform assembly. The vacuum-held preform assembly can thenbe consolidated by heating in a furnace to just above the glasssoftening temperature so that the glass cladding section(s), the corecanes, and the top and bottom caps, which are all made of glass, seal toone another. In addition, the glass flow can remove the internalchamber. The result is a solid glass preform that is ready to be drawn,especially if the furnace used for the consolidation is a draw furnaceused for drawing optical fiber.

Additionally, if an outer common cladding is to be included, thematerial that will become the outer common cladding may be added to theouter surface of the preform containing the cores. For instance, sootmay be applied to the preform via organic vapor deposition and thenconsolidated with the desired dopant. After the cores, inner commoncladding material, and outer common cladding material are assembled asabove, the coupled-core multicore optical fibers may then be drawn tothe desired fiber diameter, as described above.

The coupled-core multicore optical fibers described herein will now befurther described with reference to the following examples.

EXAMPLES Fabrication of Coupled-core Multicore Optical Fibers

The coupled-core multicore optical fiber shown in FIG. 2 was fabricatedas follows. A core cane was drawn to an outer diameter of 5 mm and alength of 120 mm. In general, the core cane was composed ofpotassium-doped silica in which the potassium concentration was from 150ppm to 250 ppm. The core cane was cut into four sections having a lengthof 30 cm. Separately, an inner common cladding preform with a targetouter diameter of 28 mm was fabricated and doped with 1.11 wt.% fluorineduring consolidation such that the refractive index delta (i.e.,Δ_(ICC)%) was -0.34% relative to pure silica. Four 5 mm holes weredrilled into the fluorine-doped preform. The centers of the holes weresymmetrically located 5.9 mm away from the central axis of the preform.The core cane sections were inserted into the holes drilled into theinner common cladding preform, and a 35 mm lead and tail section of adummy preform were added to create a 1 m preform with an outer diameterof 28 mm. Soot was applied to the inner common cladding preform viaoutside vapor deposition, and doped with 0.95 wt.% fluorine duringconsolidation to create a fluorine-doped outer common cladding with anouter diameter of 53 mm and a relative refractive index delta of -0.29%relative to pure silica around the inner cladding preform. Optical fiberwas then drawn from the preform with a cladding diameter of 125 µm. Thediameters of the cores and common inner cladding in the drawn fiber hadthe same 125 µm/53 mm scaling ratio and are 11.8 µm and 66 µm,respectively.

Characterization of Exemplary Coupled-core Multicore Optical Fibers

Six coupled-core multicore optical fibers were fabricated as detailedabove in a 2 × 2 core (“four core”) arrangement as depicted in FIG. 5A.The four cores were symmetrically disposed about the central fiber axis12. These example coupled-core multicore optical fibers werecharacterized by obtaining their refractive index profiles to obtainΔ_(CLI,) Δ_(CI), Δ_(ICC,) and Δ_(OCC,) all in %, as well as r_(CL1),r_(C1), and R_(ICC,) all in µm. The results are presented in Table 1.The geometric parameters, including overall fiber diameter in µm, andthe core-to-core distance (“core pitch”) in µm were also determined.Physical characteristics, including the effective area (A_(eff)) of thecores in µm², the average attenuation in dB/km, the cable cutoff in nmof each core, average 1 × 15 mm diameter bend loss at 1550 nm indB/turn, average 1×20 mm diameter bend loss at 1550 nm in dB/turn,average 1×30 mm diameter bend loss at 1550 nm in dB/turn,zero-dispersion wavelength in nm of each core, the dispersion at 1310 nmin ps/nm/km of each core, dispersion slope at 1310 nm in ps/nm²/km ofeach core, the dispersion at 1550 nm in ps/nm/km of each core, and thedispersion slope at 1550 nm in ps/nm²/km of each core, were alsodetermined. Additionally, the concentration of fluorine in therespective claddings in wt.% was determined. The characterization dataare tabulated in Table 1. The refractive index profile of Example 1prior to being drawn and scaled to the dimensions anticipated in theoptical fiber is shown in FIG. 8 . The refractive index profile ofExample 2 after being drawn is shown in FIG. 9 . The refractive indexprofile of Example 3 after being drawn is shown in FIG. 10 . Therefractive index profile of Example 4 prior to being drawn and scaled tothe dimensions anticipated in the optical fiber is shown in FIG. 11 .The refractive index profile of Example 5 prior to being drawn is shownin FIG. 12 . The refractive index profile of Example 6 prior to beingdrawn and scaled to the dimensions anticipated in the optical fiber isshown in FIG. 13 . The radii and percent delta values of the indexprofiles shown in FIGS. 8-13 are labeled similarly to those of FIG. 7A.

TABLE 1 Example 1 2 3 4 5 6 Δ_(CL1) (%) 0.114 0 0 0.114 0.085 0.134r_(CL1) (µm) 1.15 2.22 2.22 1.409 2.13 2.69 Δ_(C1) (%) -0.068 -0.039-0.039 -0.071 -0.071 -0.073 r_(C1) (µm) 4.41 6.845 8.14 5.752 6.12 7.27Δ_(ICC)(%) R_(ICCX) (µm) 15.5 17.57 19.43 21.26 22.64 26.57 Δ_(OCC) (%)-0.44 -0.273 -0.253 -0.308 -0.305 -0.287 F wt % core and inner claddingportions 1.47 1.04 0.83 1.18 -1.06 1.08 Max F wt% inner common claddingportion 1.63 1.24 1.01 1.18 1.06 1.08 F wt% in outer common cladding1.47 0.91 0.84 1.03 1.02 0.96 Fiber Diameter R_(OCC) (µm) 125 125 125125 125 125 Core-to-core minimum distance (core pitch) (µm) 31 35.1438.84 42.51 45.28 53.14 Core-to-core maximum distance (core pitchbetween diagonally adjacent cores) (µm) 63.63 63.63 63.63 63.63 63.6363.63 A_(eff) at 1550 nm (µm²) of each core 73.54 115 150 111 122.8 136Average Attenuation at 1550 nm (dB/km) 0.165 0.165 0.165 0.165 0.1650.165 Cable cutoff (nm) of each core 1219 1393 1528 1353 1364 1528Average 1×15 mm diameter bend loss (dB/turn) 0.529 1.23 1.38 1.9 3.840.859 Average 1×20 mm diameter bend loss (dB/turn) 0.103 0.306 0.3080.46 0.923 0.202 Average 1×30 mm diameter bend loss (dB/turn) 0.00170.018 0.008 0.02 0.029 0.01 Zero-dispersion wavelength (nm) of each core1313 1285 1284 1290 1291 1285 Dispersion at 1310 nm (ps/nm/km) of eachcore 0.388 3 3.07 2.5 2.4 3 Dispersion slope at 1310 nm (ps/nm²/km) ofeach core 0.0867 0.09 0.091 0.088 0.0889 0.092 Dispersion at 1550 nm(ps/nm/km) of each core 17.17 20.66 21.03 19.97 19.96 20.94 Dispersionslope at 1550 nm (ps/nm²/km) of each core 0.058 0.06 0.062 0.06 0.0610.063

Examples 1, 3, 5, 6 were also examined to determine the couplingcoefficient and the crosstalk between adjacent cores in dB with variouscore-to-core spacing. The coupling coefficients were determined bycalculating the overlap integral between the electric fields of the LP01modes in two neighboring cores. The crosstalk was calculated based onEquation (7). The results are summarized in Table 2 (couplingcoefficients) and Table 3 (crosstalk). From the two tables, it ispossible to choose the core spacing for a profile design to achieve adesired coupling coefficient and crosstalk. For coupled core multicoreoptical fibers, the core spacing can provide a coupling coefficientgreater than or equal to 3.4 × 10⁻⁴ /m, greater than or equal to 1.1 ×10⁻³ /m, or even greater than or equal to 2.5 × 10⁻³ /m. The crosstalkis greater than or equal to -20 dB, greater than or equal to -10 dB, oreven equal to 0 dB.

TABLE 2 Coupling coefficients (per meter) Core spacing (µm) Example 1Example 3 Example 5 Example 6 15 158.7685 509.718 333.266 380.7536 2024.62562 101.1711 71.81051 77.00593 25 3.819529 20.08087 15.4733815.57415 30 0.592424 3.985739 3.334127 3.149811 35 0.091887 0.7911070.718421 0.637037 40 0.014252 0.157022 0.154802 0.128838 45 0.0022110.031166 0.033356 0.026057 50 0.000343 0.006186 0.007187 0.00527 555.32E-05 0.001228 0.001549 0.001066 60 8.25E-06 0.000244 0.0003340.000216

TABLE 3 Crosstalk (dB) Core spacing (µm) = Example 1 Example 3 Example 5Example 6 15 0 0 0 0 20 0 0 0 0 25 0 0 0 0 30 0 0 0 0 35 -10.7 0 0 0 40-26.9 -6.1 -6.2 -7.8 45 -43.1 -20.1 -19.5 -21.7 50 -59.3 -34.2 -32.9-35.6 55 -75.5 -48.2 -46.2 -49.4 60 -91.7 -62.3 -59.5 -63.3

As shown in Examples 2-6, the optical fibers described herein arecapable of achieving an effective area A_(eff) for each core of greaterthan 100 µm² at 1550 nm. And in some instances, the A_(eff) of each coremay be much greater, such as with Example 3, which has an A_(eff) foreach core of 150 µm². However, the average attenuation remainedrelatively low in all the examples, i.e., 0.165 dB/km. The attenuationwould be expected to be higher if there were significant levels ofcrosstalk present, but this undesirable phenomenon is suppressed throughoptimization of the refractive indices and dimensions of the cores andcladdings and the spacing between the cores.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the embodiments describedherein without departing from the spirit and scope of the claimedsubject matter. Thus it is intended that the specification cover themodifications and variations of the various embodiments described hereinprovided such modification and variations come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A coupled-core multicore optical fibercomprising: an outer common cladding comprising a relative refractiveindex Δ_(OCC) relative to pure silica; and a plurality of cores disposedin the outer common cladding, each of the plurality of cores comprisingan inner core portion comprising a relative refractive index A_(Ci)relative to pure silica and a maximum relative refractive index Δ_(CLi)relative to pure silica; wherein: Δ_(CLi) > Δ_(Ci) > Δ_(ICC); each ofthe inner core portions comprises greater than or equal to 0.02 wt.% andless than or equal to 0.15 wt.% fluorine; a distance between centers ofan adjacent two of the plurality of cores is greater than or equal to 20micrometers (µm) and less than or equal to 40 µm; and a couplingcoefficient κ between adjacent cores in the plurality of cores isgreater than or equal to 1 × 10⁻³ /m.
 2. The coupled-core multicoreoptical fiber of claim 1, wherein a distance between centers of anadjacent two of the plurality of cores is greater than or equal to 45 µmand less than or equal to 65 µm.
 3. The coupled-core multicore opticalfiber of claim 1, wherein a crosstalk between the plurality of cores isgreater than or equal to -50 decibels (dB) per kilometer.
 4. Thecoupled-core multicore optical fiber of claim 1, comprising greater thanor equal to 2 and less than or equal to 6 of the cores.
 5. Thecoupled-core multicore optical fiber of claim 1, comprising 3 sets of 3of the cores.
 6. The coupled-core multicore optical fiber of claim 1,wherein a cable cutoff wavelength of each of the plurality of cores ofthe optical fiber is greater than or equal to 1200 nanometers (nm) andless than or equal to 1520 nm.
 7. The coupled-core multicore opticalfiber of claim 1, wherein an average bend loss of the plurality of coresof the optical fiber at a wavelength of 1550 nm measured on a mandrelhaving a diameter of 20 millimeters (mm) is greater than or equal to0.01 decibels per turn (dB/turn) and less than or equal to 1 dB/turn. 8.The coupled-core multicore optical fiber of claim 1, wherein an averagebend loss of the plurality of cores of the optical fiber at a wavelengthof 1550 nm measured on a mandrel having a diameter of 30 mm is greaterthan or equal to 0.001 decibels per turn (dB/turn) and less than orequal to 0.03 dB/turn.
 9. The coupled-core multicore optical fiber ofclaim 1, wherein a minimum distance between a center of one of theplurality of cores to an adjacent edge of the optical fiber along a lineformed by a centerpoint of the optical fiber, the center of the one ofthe plurality of cores, and the adjacent edge in a plane perpendicularto a long axis of the coupled-core multicore optical fiber is greaterthan or equal to 30 µm and less than or equal to 50 µm.
 10. Thecoupled-core multicore optical fiber of claim 1, wherein each of theplurality of cores comprises an inner cladding portion and an inner coreportion corresponding to the inner cladding portion, each inner claddingportion surrounding the corresponding inner core portion.
 11. Thecoupled-core multicore optical fiber of claim 10, wherein each innercladding portion comprises a relative refractive index Δ_(ICi), theinner core portion comprises the Δ_(CLi), and Δ_(CLi) > Δ_(Ci) >Δ_(ICi) > Δ_(OCC).